Problem: Simplify the following expression: $p = \dfrac{-4n^2 - 28n - 48}{n + 3} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-4$ , so we can rewrite the expression: $ p =\dfrac{-4(n^2 + 7n + 12)}{n + 3} $ Then we factor the remaining polynomial: $n^2 + {7}n + {12} $ ${3} + {4} = {7}$ ${3} \times {4} = {12}$ $ (n + {3}) (n + {4}) $ This gives us a factored expression: $\dfrac{-4(n + {3}) (n + {4})}{n + 3}$ We can divide the numerator and denominator by $(n - 3)$ on condition that $n \neq -3$ Therefore $p = -4(n + 4); n \neq -3$